The invention relates generally to processing of numerical data which characterize subsurface earth formations. More particularly, the invention relates to a method and a system for removing high order free surface multiples from a seismic shot record using a genetic algorithm.
A seismic record normally registers several different types of signals and noises during acquisition of the data. Primary reflections, representing seismic energy that has been reflected once from an interface in the subsurface, are the events that are used to map the subsurface. During seismic processing it is important to remove those recorded events that interfere with the primary seismic energy. One of the most important seismic noises that must be attenuated in processing is that of multiple events. Multiple events are generated when seismic energy undergoes three or moire reflections in the subsurface. Surface multiple energy arises when seismic energy which has been reflected one or more times in the subsurface, and is returning upward towards the surface, is reflected back into the subsurface by the normally large reflectivity of the air-surface interface, then is reflected back again towards the surface, and then is recorded. Internal multiple energy refers to any seismic event that has undergone multiple reflections from two or more interfaces into the subsurface. The problem addressed herein is concerned with the removal of surface multiple energy only.
Accordingly, given a set of measured seismic field data, D.sub.o (x,t), with primary reflections and free surface multiples, improved techniques are desired for determining a new data set, D.sub.p (x,t), that contains primaries-only reflection events. Traditional techniques for supressing free surface multiples involve calculations utilizing an estimate of the inverse of the source wavelet made from the seismic data, and utilizing linear estimation techniques that are both complicated to automate and inaccurate. Other techniques employ nonlinear optimization techniques to find a suitable solution to the inverse source waveform. Notable among these is the work of Carvalho who used a simulated annealing algorithm to extract the inverse wavelet. See Paulo M. Carvalho and Arthur B. Weglein, Wavelet Estimation for Surface Multiple Attenuation Using a Simulated Annealing Algorithm, Sixty Fourth Annual Int'l Meeting, Soc'y of Exploration Geophysicists, Expanded Abstracts 1481-84 (1994).
By way of further background, optimization methods known as "genetic algorithms" have been applied to non-linear problems in many diverse areas, including operation of a gas pipeline, factory scheduling and semiconductor layout. Genetic algorithms serve to select a string (referred to as a "chromosome") of numbers ("genes") having values ("alleles") that provides he optimum value of a "fitness function." According to this technique, a group of chromosomes (a "generation") is first randomly generated, and the fitness function is evaluated for each chromosome. A probability function is then produced to assign a probability value to each of the chromosomes according to its fitness function value, so that a chromosome with a higher fitness function value obtains a higher probability. A "reproduction pool" of chromosomes is then produced by random selection according to the probability function; the members of this reproduction pool are more likely to be selected from the higher fitness function values. A randomly selected chromosome from the reproduction pool then "reproduces" with another, randomly selected, chromosome in the reproduction pool by exchange of genes at a randomly selected "crossover" point in the chromosome. This reproduction is repeated to generate a second generation of chromosomes. Mutation may be introduced by randomly altering a small fraction of the genes in the second generation (e.g., one in one thousand). The fitness function is then evaluated for each of the chromosomes in the second generation, and the reproduction process is repeated until the desired convergence is obtained.
Over the years, researchers have developed many different variants of the original genetic algorithm implementation. The algorithm described above is one implementation that may be used to solve oil field related analysis problems, such as determining material balance in a production operation. A second variant of the genetic algorithm methodology, a so-called "Bit Climber," may also be applied. The Bit Climber provided a solution with accuracy equal to that achieved with the first genetic algorithm procedure and improved computer speed. See Lawrence Davis, Bit-Climbing, Representational Bias and Test Suite Design, 1991 Proceedings of the Fourth Int'l Conf. on Genetic Algorithms, U.C. San Diego 18-23, which is hereby incorporated by reference in its entirety.
What is needed, therefore, is a technique of estimating the inverse source wavelet of a seismic shot record for improved accuracy and efficiency in removing high order free surface multiples from the shot record.